Question

Let f be a continuous function on the real line. Suppose f is uniformly continuous on...

Let f be a continuous function on the real line. Suppose f is uniformly continuous on the set of all rationals. Prove that f is uniformly continuous on the real line.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
. Let I and J be two non-degenerate intervals and suppose that f is uniformly continuous...
. Let I and J be two non-degenerate intervals and suppose that f is uniformly continuous on I and J. Prove that if I ∩J 6= then f is uniformly continuous on I ∪ J.
We know that any continuous function f : [a, b] → R is uniformly continuous on...
We know that any continuous function f : [a, b] → R is uniformly continuous on the finite closed interval [a, b]. (i) What is the definition of f being uniformly continuous on its domain? (This definition is meaningful for functions f : J → R defined on any interval J ⊂ R.) (ii) Given a differentiable function f : R → R, prove that if the derivative f ′ is a bounded function on R, then f is uniformly...
Suppose A is bounded and not compact. Prove that there is a function that is continuous...
Suppose A is bounded and not compact. Prove that there is a function that is continuous on A, but not uniformly continuous. Give an example of a set that is not compact, but every function continuous on that set is uniformly continuous.
Let f: (0,1) -> R be uniformly continuous and let Xn be in (0,1) be such...
Let f: (0,1) -> R be uniformly continuous and let Xn be in (0,1) be such that Xn-> 1 as n -> infinity. Prove that the sequence f(Xn) converges
Prove that the function f(x) = x2 is uniformly continuous on the interval (0,1).
Prove that the function f(x) = x2 is uniformly continuous on the interval (0,1).
let F : R to R be a continuous function a) prove that the set {x...
let F : R to R be a continuous function a) prove that the set {x in R:, f(x)>4} is open b) prove the set {f(x), 1<x<=5} is connected c) give an example of a function F that {x in r, f(x)>4} is disconnected
A function f : A −→ R is uniformly continuous and its domain A ⊂ R...
A function f : A −→ R is uniformly continuous and its domain A ⊂ R is bounded. Prove that f is a bounded function. Can this conclusion hold if we replace the "uniform continuity" by just "continuity"?
Let f be a continuous function. Suppose theres a sequence (x_n) in [0,1] where lim f(x_n))=5....
Let f be a continuous function. Suppose theres a sequence (x_n) in [0,1] where lim f(x_n))=5. Prove there is a point x in [0,1] where f(x)=5.
prove that this function is uniformly continuous on (0,1): f(x) = (x^3 - 1) / (x...
prove that this function is uniformly continuous on (0,1): f(x) = (x^3 - 1) / (x - 1)
Find the constant a such that the function is continuous on the entire real line. f(x)...
Find the constant a such that the function is continuous on the entire real line. f(x) = 8x2,      x ≥ 1 ax − 3,      x < 1
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT